Introduction to the nmr-cycling technique and basic instrumentation

INTRODUCTION TO THE NMR
FIELD-CYCLING TECHNIQUE AND
BASIC INSTRUMENTATION
ESTEBAN ANOARDO
anoardo@famaf.unc.edu.ar
FaMAF – UNC
IFFAMAF – CONICET
CORDOBA - ARGENTINA

Relaxometry: Larmor frequency
dependence of a given NMR
relaxation parameter
Example: T 1 =f(ν 0 ) spinlattice
relaxation time
ν 0 = γ.Β/2π

What is field-cycling?
Defines ν 0

Why magnetic field cycling in NMR
experiments?

Signal to noise ratio in
NMR experiments
B(t)
t
B(t)
t

Example 1: field-cycling NMR relaxometry
100
100
Bulk 8CB
ISOTROPIC 323K
NEMATIC 309K
T 1
[ms]
90
80
70
8CB+Aerosil
8CB Bulk
T 1
[ms]
10
υ 1/2
60
50
323K
1 10 100 1000 10000
ν 0
[kHz]
0.1 1 10 100 1000 10000
ν 0
[kHz]

Example 2: nuclear quadrupole double
resonance (NQDOR)
Ho
POLARIZATION
DETECTION
100
80
60
IRRADIATION
40
20
0
A
HpAB / 82 o C
SMECTIC
300 400 500 600 700
ωQ
t

Example 3: zero field NMR

Example 4: electron-nuclear double resonance
(ENDOR)
CRITIC FOR ELECTRONS
ZFR
X-BAND

Quadrupole dips
NQR frequencies
I=1
ν +
T CR
H Z
H Q
ν -
ν o
ν -
Larmor
frequency
I=1/2
T Z
Lattice
T Q
DIP
1
DIP
2
External magnetic field
DIP
3

Example 5: field-cycling MRI
T 1 dispersion plot of volunteer’s thighs
FC inversion recovery images
T1 (ms)
210
200
190
180
170
160
14
N-NQDips
B 0e =
65 mT
150
140
30 40 50 60 70 80
Evolution field (mT)
B 0e =
75 mT
Data acknowledged to David Lurie (Aberdeen)

Field-cycling: the roots
1949-1951:
Turner and Sachs, Ramsey and Pound
(Cambridge).
Hebel, Slichter and Lurie (Illinois).
Hahn @IBM Watson Lab (New York).
1950s:
At IBM: Redfield, Anderson, Kung and Genak:
relaxometry.
Hahn: NQR.
1960s:
Fite, Bleich and Redfield and later Koenig,
Brown and Kiselewsky at IBM.
Noack - Kimmich: relaxation spectroscopy
(Stuttgart).
Hahn (Berkeley).
E. M. Purcell
F. Noack
E. L. Hahn
C. P. Slichter

Stelar
1997: first prototype
“Spinmaster FFC”
2000: FFC-2000
2003: 1T magnet
2006: Compact version
2006: SMARtracer

Basic Experiment: measurement
of the Larmor frequency
dependence of T 1

T 1
B o
t=0
SAMPLE
M
B o
t=τ

Signal
intensity
MAGNETIZATION DECAY
Magnetic
Field cycle
time
T 1
T 1
Defines de Larmor frequency!
time
frequency

What do we measure?
Magnetization decay
1,2
1,0
0,8
0,6
0,4
Data: D ata1_B
M odel: ExpD ec1
y0+A1e^(-x/t1)
Chi^2 = 0.00011
R^2 = 0.99905
y0 0.19773 ±0.00563
A1 0.99187 ±0.01106
t1 0.99018 ±0.026
∆t1=2,6%
T 1 or 1/T 1 = R 1 ?
Y0+A1e^(-r1x)
0,2
0 1 2 3 4 5 6
Effective relaxation delay

About the magnetic field sequence
1,2
1,0
Magnetization decay
0,8
0,6
0,4
Data: Data1_C
Model: ExpDec1
y0+A1e^(-x/t1)
Chi^2 = 7.7417E-6
R^2 = 0.99327
y0 0.99729 ±0.00151
A1 0.09907 ±0.00294
t1 1.00385 ±0.07037
∆t1=7%
0,2
0 1 2 3 4 5 6
Effective relaxation delay

Magnetization evolutions with same T 1
Relaxation field level
Zero field level

Signal
intensity
MAGNETIZATION GROW
Magnetic
Field cycle
time
T 1
Etc
T 1
Defines de Larmor frequency!
time
frequency

PP sequence

NP sequence

B a s ic p r e p o la r is e d s e q u e n c e
B p
B d
B r
P W
T x
A c q
How is obtained the relaxation curve
EWIB
EWEB
d p d f d r d o
B a s ic n o n p o la r is e d s e q u e n c e
Mk
B = 0
T x
A c q
B r
B d
P w
EWIP EWEP
τ
Fitted
curve
d p d f d r d o
Source: Stelar

Switching times
Magnetization decay
1,2
1,0
0,8
0,6
0,4
Data: Data1_B
Model: ExpDec1
y0+A1e^(-x/t1)
Chi^2 = 0.00011
R^2 = 0.99905
y0 0.19773 ±0.00563
A1 0.99187 ±0.01106
t1 0.99018 ±0.026
0,2
0 1 2 3 4 5 6
Effective relaxation delay

T 1 relaxation
dispersion [s]
T 1 profile
Relaxation rate (1/T 1
- 1 1 or R 1 ) dispersion [s ]
NMRD: nuclear
magnetic relaxation
dispersion
NMRD profile
Glossary
T 1
[ms]
T 1
-1
[s
-1
]
100
90
80
70
60
50
8CB+Aerosil
8CB Bulk
323K
10 100 1000 10000
ν 0 [kHz]
T=323K
8CB+AEROSIL
8CB BULK
10 1
Relaxivity: relaxation rate
for a given concentration
in a solution [mM -1 s -1 ]
10 0 10 1 10 2 10 3 10 4
ν 0
[kHz]

Hardware

Different approaches
High detection field
Superconducting magnet
Keep spectroscopic
resolution
Typical switching times
50ms – 500ms
Movable sample
Pneumatic or mechanic
system
Moderate detection field
Air-cored electromagnet
Low resolution, relaxation
applications
Typical switching times
0.2ms – 2ms.
Sample at fixed position
Power electronics
Fast-Field-Cycling (FFC)

Block-diagram
Cooling
System
Cooling
enclosure
Magnet
Magnet
Power
Supply
Probe
Preamp
VTC
Software
HOST
COMPUTER
AQM
RF unit
PULSER

I- Power network

Basic circuit
R high
L
R low
R
V 0
d I
1
= V
0
I ( t )( R
h ig h
R )
d t L ⎡ − + ⎤
⎣ ⎦ Low-to-high

Capacitor assistance
C
LOGIC
R high
V C
Vc » Vo
V 0
L R low
R

Subdamped
i
R high
1,4
1,2
C=0.5
C=1
V 0
L R low
R
i R 0 2 4 6 8 10
R s
C
i C
ion(t) (au)
1,0
0,8
0,6
0,4
C=0
C=0.25
0,2
0,0
t (atu)

Examples

Mosfet – GTO. Energy-storage.
GTO
-
V 0
CONTROL
ELECTRONICS
v(t)
+ +
R
M
-
H.V.
r(t)
v(t)
C

+ +
-
-
+ +
-
-

Mosfet-driven network without
energy storage capacitor
+
V2
-
V 1
v(t)
S
-
+
CONTROL
ELECTRONICS
M
r(t)
v(t)

Typical Mosfet-bank

II- Magnet

Premises of design
Low inductance and resistance.
Good magnetic field to power ratio (G-factor).
NMR homogeneity.
Efficient cooling.
Simple mechanical assembly.

Field-cycling magnets
z
dr
dB
dz
2l
r 0
r 1

The Dvinskikh-Molchanov
approach (1985)
COOLANT IN
WINDING
COOLANT
OUT
y
x
PROBE

Schweikert-Noack Magnet (1989)

• Inversion of the Biot-Savart law
• Lagrange minimization procedure:
• Lagrange minimization procedure:
field to power ratio, homogeneity and volume

10 layer magnet (Stuttgart-Córdoba, 1992)

Notch-coilcoil
Rommel - Seitter -
MOVABLE
OUTER COILS
Kimmich
(1993-1995) 1995)
VARIABLE
GAP
DOUBLE
WINDING
LAYERS
MAGNET
BORE

Stelar 2L-0.5T system (1997-2000)

Stelar 4L-1T system (2003)

Magnet cooling
45
40
15 o C
18 o C
12MHz
35
C]
Thermal Jump [ o
30
25
20
15
10
5
10MHz
8MHz
5MHz
0
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Polarization Time [s]

ULF regime
External magnetic field components:
magnetic field compensation.
Internal magnetic field components: local
fields.

Switching the Zeeman Field
z l
z
B 0
(t)+B P
B(t)
B 0
(t)
B P
B
α(t)
y l
y
B N
x l
S
x

Time-dependence of the field
12
10
8
B pol
=10MHz
B det
=9.3MHz
B 0
[MHz]
6
4
RELAXATION
DELAY
2
0
A
t sw
B rel
=10kHz
B 0
[kHz]
80
70
60
5 10 15 20 25 30
t [ms]
50
40
30
20
10
0
-10
16 17 18 19 20 21 22 23
t [ms]
B

30
25
40
20
35
15
Shunt Voltage [mV]
30
25
20
15
10
5
0
1.6ms
100kHz=10mV
50kHz
Shunt Voltage [mV]
10
5
0
-5
-10
30
25
20
15
100kHz
Slew Rate 14MHz/ms
0,012 0,013 0,014 0,015 0,016
-5
0,012 0,013 0,014 0,015 0,016 0,017
Sequence Timing [s]
10
5
0
100kHz
Slew Rate 12MHz/ms
-5
-10
0,012 0,013 0,014 0,015 0,016
Sequence Timing [s]

Adiabatic & non-adiabatic
switching
20
Signal Amplitude [au]
15
10
5
B r
=4kHz
B r
=7kHz
0
0.000 0.005 0.010 0.015 0.020 0.025
τ[s]

Magnetic field compensation
GdCl3 2mM 294K
Signal Signed Magnitude [au]
8
6
4
2
0
-2
-4
-6
-8
8
6
4
2
0
-2
-4
-6
-8
8
6
4
2
0
-2
-4
-6
-8
B offset
= +4.4kHz
A
0,00 0,01 0,02 0,03 0,04
B offset
= 0kHz
B
0,00 0,01 0,02 0,03 0,04
B offset
= -7.8kHz
C
0,00 0,01 0,02 0,03 0,04
NAFID Signal Intensity [au]
9
8
7
6
5
4
5
6
7
8
9
180
150
210
120
240
90
270
60
300
30
330
τ [s]

Automatic compensation
y (cm)
9
6
3
0
-3
-6
-9
-9 -6 -3 0 3 6 9
x (cm)
G x
(G/cm)
-3E-4
-1.8E-4
-6E-5
6E-5
1.8E-4
3E-4
Amp.[a.u.]
Amp.[a.u.]
Amp.[a.u.]

Plateaus and false dispersions
0.1
A
T 1 [s]
0.01
5CB - 303K
13kHz
1E-4 1E-3 0.01 0.1 1 10
0.1
B
0.01
21kHz
5CB - 298K
1E-4 1E-3 0.01 0.1 1 10
ν 0
[MHz]

Sources for low-frequency plateau
Plateau
Cut-off of the effective
relaxation mechanism
Hardware
Local Fields
Current Offset in
the Magnet
Magnetic Field Offset
Magnetic Field
time dependence
Dipolar
Quadrupolar

Local Field Plateau
T 1
(ν 0
)=A.((ν 0
+ (ν L 2 - ν N 2 ) 1/2 ) 2 + ν N 2 ) 1/2 ν 0
0.5
10
T 1 [a.u]
ν L
20kHz
10kHz
5kHz
ν N
=0
ν N
=ν L
1
0.1 1 10 100 1000
ν 0
[kHz]

Local
fields
• Plateau
• Data scattering
Liposomes
DMPC – D 2 O 100nm

Yesterday and today….

R. E. Slusher (1966): “The author is shown in typical
operating position with an instrument used to sooth the
electric apparatus (and the author)”
Source: Slusher´s Thesis (E. Hahn lab)

Stuttgart Instrument by 1970
Pictures from R. Kimmich

“Relaxometry”
The IBM first
Prototype, as later upgraded
at the University of Florence
Alfred Redfield
Relaxation theory 1957
Sorce: internet

Córdoba, 1993

Ulm, 1995-2000

1998

Stelar (Mede – Italy): first prototype FFC-2000

FFC-2000

Compact version

SMARtracer
Stelar Magnetic Relaxation tracer

Basic literature
F. Noack Progr. NMR Spectrosc. 18, 171 (1986).
R. Kimmich, NMR Tomography, Diffusometry,
Relaxometry. Springer. Berlin (1997).
E. Anoardo, G. Galli and G. Ferrante, Appl. Magn.
Reson. 20, 365 (2001).
R. Kimmich and E. Anoardo, Prog. NMR Spectrosc. 44,
257 (2004).
G. Ferrante and S. Sykora, Adv. Inorg. Chem. 57, 405
(2005).